THE University of Texas made headlines across the country in 1978 with its purchase of a rare, perfect edition of the Gutenberg Bible. The school's $2.4 million expenditure for one book exemplified, according to various commentaries, a new striving for recognition and world-class status. Crowed one exultant Texas representative: ``It's instant ivy!'' Reminded of that story today, University of Texas at Austin president William Cunningham simply smiles, as one often does when remembering simpler times and youthful ambitions. Gone are the days when the purchase of a book, or the wooing of one big name to the faculty, would be considered enough to vault the university to international status. Gone, too, apparently, is the political meddling that in the '60s and early '70s made ``academic freedom'' a laughable concept here.

Looking over the past decade, Dr. Cunningham says, ``We have learned that progress is sometimes slower than we would like. Greatness takes time and is difficult to achieve and maintain.'' The infectiously upbeat, four-year chief executive adds, ``From our sense of maturity, however, comes a confidence that our goals are realistic.''

After a roller-coaster decade of tremendous growth, unprecedented outlays for top faculty, and some disconcerting setbacks, UT Austin - with more than 50,000 students, and more graduate students than total enrollment at Stanford University - finds itself at an important crossroads.

The university has taken on an impressive and growing role in setting the course of development for the state it calls home. It is at least partly responsible for a concentration of technological research in Texas.

On the other hand, the university faces a debilitating increase in enrollment - up more than 10 percent in the past two years alone - that many here believe could derail its quest for excellence. An unwillingness to seriously limit enrollment, coupled with the state's failure to place the institution's finances on sound footing beyond a traditional reliance on oil and gas revenues, forms a worrisome question mark on the Longhorns' horizon.

Since the oil boom of the '70s started a gusher of revenue to university coffers, world-renowned scholars and impressive new buildings have been added to the 365-acre campus. Some disciplines, like Spanish, botany, and Germanic studies, are among the best in the country. But at the same time, some of school's largest departments, including English, history, and economics, are considered weak, in part because they must educate the expanding undergraduate population. In addition, financial support for the liberal arts has trailed that of scientific endeavors, which state leaders appear to equate with economic development.

University officials hope to see freshmen enrollment, which reached 6,700 this academic year, fall to 6,000 in the fall of '89. But some foresee a total student population of 53,000 by the early '90s. With the university operating on a budget intended for a student population of 46,000, the result is overcrowded classes, meager administration, and thinly spread student services. ONE reason UT now faces such a difficult overcrowding problem is that it never received the resources to develop a system of branch campuses, as did the University of California, that students would consider competitive alternatives to the mother campus. Austin is the flagship of a 14-branch system, but Texas's top high school graduates do not generally consider other locations as alternatives to Austin.

Although tax dollars don't flow as freely to the university as they do in other large states, a gush of oil money has allowed the University of Texas to sit among the top public universities in the country. UT's huge endowment, which it shares with Texas A&amp;M University, is largely composed of west Texas oil lands - three times the size of Rhode Island - the university owns.

Conservatively estimated two years ago by Forbes magazine to be worth more than $8 billion, but officially ranked second only to Harvard's, UT's endowment has allowed construction of a state-of-the-art campus. In the last decade, income from the endowment has also been used to match private donations to create endowed faculty positions.

Since 1980, 875 of UT's 987 endowed faculty positions have been created, with 74 of them endowed at $1 million or more.

There is, however, a down side to the monetary flow from the university's endowment: The increase has been counterbalanced by a decrease in state revenues allocated to UT. Annual tax-generated revenue has declined by $26 million, or more than 12 percent, over the last four years. In 1985, state tax dollars paid for 44.7 percent of the university's operations, compared with 31.5 percent today.

What one faculty member termed UT's ``unresolved paradox'' is that Texans want a great university - for their children, for economic development - but they don't want taxes to pay for it. Neither do they want tuition to pay for it, apparently, since Texas ranks at the very bottom of 30 public universities in tuition costs.

UT is deeply involved in Texas's economic development, having created a partnership among the university, state government, and the private sector that is now a model for other states. ``The alliance that started with going after excellence in our faculty is now the momentum in our drive for a competitive technological base,'' says George Kozmetsky, former dean of the UT business school and founder of Teledyne Corp.

Despite this enthusiasm, others, especially in UT's College of Liberal Arts, worry that ``economic development'' is being too strictly defined, and that little provision is being made for the traditional liberal arts in the university's love affair with business and the sciences. ``Many of us are apprehensive as to what the future holds for the college,'' says one professor who asked that his name not be used. ``We don't see much recognition of what role the liberal arts play in a great university.''

That view is not universally held, however, and there are signs that at least some parts of liberal arts are receiving renewed attention.

The government department is one that until recently suffered from internal contention and big-name departures. But this year it has a new chairman, several new recruits, and a new infusion of financial support.

``The administration has not diluted its vision of a great university, and it's been wonderfully supportive of this department,'' says James Fishkin, named government department chair this year. Dr. Fishkin, who came to UT from Yale five years ago, says a good recruiting year in 1988 will be followed by another this year. ``People are excited about coming here and building something.''

As university officials from President Cunningham on down state confidently, the potential is there for UT to be among the top two or three public universities in the country. The determining factor may be how much sacrifice the people of Texas, usually intent on being No. 1, are willing to make to get there.